Approaches that integrate experiment design, analysis, and performance will benefit a variety of measurements, including 13C-labeling studies, relaxation measurements and imaging protocols. To optimize experiments, mathematical modeling can be employed as an integral part of the scientific procedure, which contains these steps: (1) the formation of a hypothesis or question, (2) the development of an experimental plan, (3) the acquisition of data, and (4) the analysis and interpretation of data. The efficiency of an experiment and its likelihood of success are subject to its design, the quality of the data, and its interpretation, which depend on careful planning and data analysis. Therefore, experimental protocols should be designed with considerations of signal-to-noise and sensitivity to hypotheses. This project describes the development and application of quantitative approaches to experimental design, analysis, and hypothesis building for some specific areas and for general application in a wide variety of studies. In particular the project, in its 4 specific aims, seeks to develop modeling analyses for isotopic labeling experiments (13C) with the intent of optimizing NMR data acquisition for 13C studies with improved metabolite quantification and relaxation rate measurements and to investigate new approaches to design and analysis of such experiments.